The process of biological fate decision regulated by gene regulatory networks involves numerous complex dynamical interactions among many components. Mathematical modeling typically employed ordinary differential equations and steady-state analysis, which has yielded valuable quantitative insights. However, stable states predicted by theoretical models often fail to capture transient or metastable phenomena that occur during most observation periods in experimental or real biological systems. We attribute this discrepancy to the omission of dynamic processes of various complex interactions. Here, we demonstrate the influence of delays in gene regulatory steps and the timescales of the external induction on the dynamic processes of the fate decision in inducible bistable systems. We propose that steady-state parameters determine the landscape of fate decision. However, during the dynamic evolution along the landscape, the unequal delays of biochemical interactions as well as the timescale of external induction cause deviations in the differentiation trajectories, leading to the formation of new transient distributions that persist long term. Our findings emphasize the importance of considering dynamic processes in fate decision instead of relying solely on steady-state analysis. We provide insights into the interpretation of experimental phenomena and offer valuable guidance for future efforts in dynamical modeling and synthetic biology design.

中文翻译：

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诱导双稳态系统中命运决定的动态过程


由基因调控网络调节的生物命运决定过程涉及许多组成部分之间的许多复杂的动态相互作用。数学建模通常采用常微分方程和稳态分析，这产生了有价值的定量见解。然而，理论模型预测的稳定状态通常无法捕捉到实验或真实生物系统中大多数观测期间发生的瞬态或亚稳态现象。我们将这种差异归因于遗漏了各种复杂交互的动态过程。在这里，我们展示了基因调控步骤延迟和外部诱导的时间尺度对可诱导双稳系统中命运决定动态过程的影响。我们提出稳态参数决定了命运决策的景观。然而，在沿景观的动态进化过程中，生化相互作用的不等延迟以及外部诱导的时间尺度导致分化轨迹的偏差，导致形成长期持续的新的瞬态分布。我们的研究结果强调了在命运决策中考虑动态过程的重要性，而不是仅仅依赖稳态分析。我们提供对实验现象解释的见解，并为动力学建模和合成生物学设计的未来工作提供有价值的指导。